“In 1952, the growing prominence of television as a medium of mass communication was dealt with in a report of the Special Committee on Televising and Broadcasting Legislative and Judicial Proceedings (headed by the late John W. Davis). 77 A.B.A.Rep. 607 (1952). In condemning the practice of televising judicial proceedings, the Committee called attention to the fact that:”
” The attention of the court, the jury, lawyers and witnesses should be concentrated upon the trial itself, and ought not to be divided with the television or broadcast audience who, for the most part, have merely the interest of curiosity in the proceedings. It is not difficult to conceive that all participants may become over-concerned with the impression their actions, rulings or testimony will make on the absent multitude.”
“ Id. at 610. As a result of this report, and the recommendation of the Committee on Professional Ethics and Grievances, Judicial Canon 35 was amended by inserting a ban on the ‘televising’ of court proceedings and inserting the descriptive phrase ‘distract the witness in giving his testimony’ before the phrase ‘degrade the court.’ In addition, a second paragraph was added providing for the televising and broadcasting of certain ceremonial proceedings. Id. at 110-11.”
“In October, 1954, the Board of Governors authorized the appointment of a Special Bar-Media Conference Committee on Fair Trial-Free Press to meet with representatives of the press, radio, and television. The views of both sides were thoroughly explored, and were presented in detail in the September, 1956, issue of the American Bar Association Journal. [ Footnote 4/4 ] After extensive joint debate,
Home Page 381 U. S. 599
no solutions or agreements were reached. 83 A.B.A.Rep. 790-91 (1958). The Committee did report that it was convinced that”
“courtroom photographing or broadcasting or both would impose undue police duties upon the trial judge[,] . . . that the broadcasting and the photographing in the courtroom might have an adverse psychological effect upon trial participants, judges, lawyers, witnesses and juries[,] . . . [and] that partial broadcasts of trials, particularly on television, might influence public opinion which in turn might influence trial results. . . .”
“ Id. at 645.”
“Following the presentation of the Bar-Media Conference Committee report, and in connection with the consideration of a report and recommendation of a Special Committee of the American Bar Foundation created in July, 1955 (83 A.B.A.Rep. 643-45 (1958)), the House of Delegates conducted a hearing as a ‘Committee of the Whole’ during its February, 1958, session at which proponents and opponents of Judicial Canon 35 were fully heard. 83 A.B.A.Rep. 648-69 (1958). Thereafter at the August, 1958, meeting of the House of Delegates, it was decided to have a Special Committee study Canon 35 and”
“conduct further studies of the problem, including the obtaining of a body of reliable factual data on the experience of judges and lawyers in those courts were either photography, televising or broadcasting, or all of them, are permitted. . . . The fundamental objective of the Committee and of all others interested must be to consider and make recommendations which will preserve the right of fair trial.”
“83 A.B.A.Rep. 284 (1958).”
“The Special Committee filed an Interim Report and Recommendations with the House of Delegates in August,
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1962 setting forth the ‘Area and Perspective’ of its survey and studies. The report included portions of testimony by media representatives taken at a hearing held in Chicago on February 18, 1962, as well as a summary of the Committee’s informal conference with certain representatives from Colorado and Texas. In addition, the report included written comments by officers of State Bar Associations responding to a Committee survey, and certain general correspondence received by the Committee regarding Judicial Canon 35. The report also listed significant publications favoring either revision or retention of the Canon. . . . [Hereinafter cited Int.Rep. ]”
“The Special Committee thereafter submitted its final report and recommendations, concluding that the substantive provisions of Judicial Canon 35 remain valid, and ‘should be retained as essential safeguards of the individual’s inviolate and personal right of fair trial.’ . . . The Committee did recommend certain minor deletions . . . and changes . . . which were adopted by the House of Delegates, after full debate, on February 5, 1963:”
“The taking of photographs in the courtroom, during sessions of the court or recesses between sessions, and the broadcasting or televising of court proceedings [are calculated to] detract from the essential dignity of the proceedings, distract [the] participants and witnesses in giving [his] testimony, [degrade the court,] and create misconceptions with respect thereto in the mind of the public, and should not be permitted. [ Footnote 4/5 ] ”
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“A vast majority of the states have voluntarily adopted Judicial Canon 35 in one form or another, and it has been embodied in principle in Rule 53 of the Federal Rules of Criminal Procedure. In a recent Resolution of the Judicial Conference of the United States, the philosophy of Canon 35 was unanimously reaffirmed:”
” Resolved, That the Judicial Conference of the United States condemns the taking of photographs in the courtroom or its environs in connection with any judicial proceeding, and the broadcasting of judicial proceedings by radio, television, or other means, and considers such practices to be inconsistent with fair judicial procedure and that they ought not to be permitted in any federal court.”
“ Int.Rep. p. 97.”
(Footnotes numbered and partially omitted.)
[ Footnote 4/1 ]
The House of Delegates is not only the governing body of the American Bar Association; because of the presence of representatives of all State Bar Associations, the largest and most important local bar associations, and of other important national professional groups, it is in fact a broadly representative policy forum for the profession as a whole.
[ Footnote 4/2 ]
See State v. Hauptmann, 115 N.J.L. 412, 180 Atl. 809 (Ct.Err. & App.), cert. denied, 296 U. S. 649 .
[ Footnote 4/3 ]
Prior to the adoption of Judicial Canon 35, the impropriety of permitting radio broadcasts of court proceedings was recognized by the Committee on Professional Ethics and Grievances of the Association in its Opinion No. 67, March 21, 1932. The Committee had recourse to Judicial Canon 34, which provides that a judge should not administer his office “for the purpose of advancing his personal ambitions or increasing his popularity.” The Committee found that radio broadcasting of a trial changes
“what should be the most serious of human institutions either into an enterprise for the entertainment of the public or of one for promoting publicity for the judge.”
AMERICAN BAR ASSOCIATION, OPINIONS OF THE COMMITTEE ON PROFESSIONAL ETHICS AND GRIEVANCES 163 (1957).
[ Footnote 4/4 ]
42 A.B.A.J. 834, 838, 843 (1956).
[ Footnote 4/5 ]
The full text of Judicial Canon 35, as amended, is as follows:
“IMPROPER PUBLICIZING OF COURT PROCEEDINGS”
“Proceedings in court should be conducted with fitting dignity and decorum. The taking of photographs in the courtroom, during sessions of the court or recesses between sessions, and the broadcasting or televising of court proceedings detract from the essential dignity of the proceedings, distract participants and witnesses in giving testimony, and create misconceptions with respect thereto in the mind of the public and should not be permitted.”
“Provided that this restriction shall not apply to the broadcasting or televising, under the supervision of the court, of such portions of naturalization proceedings (other than the interrogation of applicants) as are designed and carried out exclusively as a ceremony for the purpose of publicly demonstrating in an impressive manner the essential dignity and the serious nature of naturalization.”
MR. JUSTICE STEWART, whom MR. JUSTICE BLACK, MR. JUSTICE BRENNAN, and MR. JUSTICE WHITE join, dissenting.
I cannot agree with the Court’s decision that the circumstances of this trial led to a denial of the petitioner’s Fourteenth Amendment rights. I think that the introduction of television into a courtroom is, at least in the present state of the art, an extremely unwise policy. It invites many constitutional risks, and it detracts from the inherent dignity of a courtroom. But I am unable to escalate this personal view into a per se constitutional
Home Page 381 U. S. 602
rule. And I am unable to find, on the specific record of this case, that the circumstances attending the limited televising of the petitioner’s trial resulted in the denial of any right guaranteed to him by the United States Constitution.
On October 22, 1962, the petitioner went to trial in the Seventh Judicial District Court of Smith County, Texas, upon an indictment charging him with the offenses of (1) swindling, (2) theft by false pretenses, and (3) theft by a bailee. After a week spent in selecting a jury, the trial itself lasted some three and a half days. At its conclusion, the jury found the petitioner guilty of the offense of swindling under the first count of the indictment. The trial judge permitted portions of the trial proceedings to be televised, under the limitations described below. He also gave news photographers permission to take still pictures in the courtroom under specified conditions.
The Texas Court of Criminal Appeals affirmed the petitioner’s conviction, and we granted certiorari, limited to a single question. The question, as phrased by the petitioner, is this:
“Whether the action of the trial court, over petitioner’s continued objection, denied him due process of law and equal protection of the laws under the Fourteenth Amendment to the Constitution of the United States, in requiring petitioner to submit to live television of his trial, and in refusing to adopt in this all out publicity case, as a rule of trial procedure, Canon 35 of the Canons of Judicial Ethics of the American Bar Association, and instead adopting and following, over defendant’s objection, Canon 28 of the Canons of Judicial Ethics, since approved by the Judicial Section of the integrated (State agency) State Bar of Texas.”
The two Canons of Judicial Ethics referred to in the petitioner’s statement of the question presented are set
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out in the margin. [ Footnote 5/1 ] But, as the Court rightly says, the problem before us is not one of choosing between the conflicting guidelines reflected in these Canons of Judicial Ethics. It is a problem rooted in the Due Process Clause of the Fourteenth Amendment. We deal here with matters subject to continuous and unforeseeable change — the
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techniques of public communication. In an area where all the variables may be modified tomorrow, I cannot at this time rest my determination on hypothetical possibilities not present in the record of this case. There is no claim here based upon any right guaranteed by the First Amendment. But it is important to remember that we move in an area touching the realm of free communication, and, for that reason, if for no other, I would be wary of imposing any per se rule which, in the light of future technology, might serve to stifle or abridge true First Amendment rights.
I
The indictment was originally returned by a grand jury in Reeves County, Texas, and it engendered widespread publicity. After some preliminary proceedings there, the case was transferred for trial to Smith County, more than 500 miles away. The trial was set for September 24, 1962, but it did not commence on that date. Instead, that day and the next were spent in hearings on two motions filed by defense counsel: a motion to bar television and news cameras from the trial and a motion to continue the trial to a later date. Those proceedings were themselves telecast “live,” and news photographers were permitted to take pictures in the courtroom. The activities of the television crews and news photographers led to considerable disruption of the hearings. [ Footnote 5/2 ] At the conclusion
Home Page 381 U. S. 605
of the hearings the motion for a continuance was granted, and the case reset for trial on October 22. The motion to bar television and news photographers from the trial was denied. [ Footnote 5/3 ]
Home Page 381 U. S. 606
On October 1, the trial judge issued an order delineating what coverage he would permit during the trial. [ Footnote 5/4 ] As a result of that order and ensuing conferences between the judge and representatives of the news media, the environment for the trial, which began on October 22, was in sharp contrast to that of the September hearings. The actual extent of television and news photography in the
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courtroom was described by the judge, after the trial had ended, in certifying the petitioner’s bill of exceptions. This description is confirmed by my understanding of the entire record, and was agreed to and accepted by defense counsel:
“Prior to the trial of October 22, 1962, there was a booth constructed and placed in the rear of the courtroom painted the same or near the same color as the courtroom, with a small opening across the top for the use of cameras. . . .”
“Live telecasting and radio broadcasting were not permitted, and the only telecasting was on film without sound, and there was not any broadcasting of the trial by radio permitted. Each network, ABC, NBC, CBS and KRLD (KLTV) Television in Tyler was allowed a camera in the courtroom. . . . The telecasting on film of this case was not a continuous camera operation, and only pictures being taken at intervals during the day to be used on their regular news casts later in the day. There were some days during the trial that cameras of only one or two stations were in operation, the others not being in attendance upon the Court each and every day. The Court did not permit any cameras other than those that were noiseless, nor were flood lights and flash bulbs allowed to be used in the courtroom. The Court permitted one news photographer with
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Associated Press, United Press International, and Tyler Morning Telegraph and Courier Times. However, they were not permitted inside the Bar, and the Court did not permit any telecasting or photographing in the hallways leading into the courtroom or on the second floor of the courthouse, where the courtroom is situated, in order that the Defendant and his attorneys would not be hindered, molested or harassed in approaching or leaving the courtroom. The Court did permit live telecasting of the arguments of State’s counsel and the returning of the verdict by the jury and its acceptance by the Court. The opening argument of the District Attorney of Smith County was carried by sound, and, because of transmission difficulty, there was not any picture. The closing argument for the State by the District Attorney of Reeves County was carried live by both picture and sound. The arguments of attorneys for Defendant, John D. Cofer and Hume Cofer were not telecast or broadcast, as the Court granted their Motion that same not be permitted.”
“There was not any televising at any time during the trial except from the booth in the rear of the courtroom, and, during the argument of counsel to the jury, news photography was required to operate from the booth so that they would not interfere or detract from the attention of either the jurors or the attorneys.”
“During the trial that began October 22nd, there was never at any time any radio broadcasting equipment in the courtroom. There was some equipment in a room off of the courtroom where there were periodic news reports given, and, throughout the trial that began October 22nd, not any witness requested not to be televised or photographed while they were testifying. Neither did any juror, while being interrogated on voir dire or at any other time, make any request of the Court not to be televised.”
Thus, except for the closing arguments for the prosecution and the return of the jury’s verdict, there was no “live” telecasting of the trial. And, even for purposes of delayed telecasting on later news programs, no words or other sounds were permitted to be recorded while the members of the jury were being selected or while any witness was testifying. No witnesses and no jurors were televised or photographed over their objection. [ Footnote 5/5 ]
Finally, the members of the jury saw no telecasts and no pictures of anything that went on during the trial. In accord with Texas law, the jurors were sequestered, day and night, from the beginning of the trial until it ended. [ Footnote 5/6 ] The jurors were lodged each night in quarters provided for that purpose in the courthouse itself. On the evening of November 6, by agreement of counsel and special permission of the court, the members of the jury were permitted to watch the election returns on television for a short period. For this purpose, a portable television was brought into the jury’s quarters by a court officer, and operated by him. Otherwise, the jurors were not permitted to watch television at any time during the trial. The only newspapers permitted the jury were ones from which all coverage of the trial had been physically removed.
II
It is important to bear in mind the precise limits of the question before us in this case. The petition for a writ of certiorari asked us to review four separate constitutional claims. We declined to review three of them, among which was the claim that the members of the jury “had received through the news media damaging and prejudicial
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evidence. . . .” [ Footnote 5/7 ] We thus left undisturbed the determination of the Texas Court of Criminal Appeals that the members of the jury were not prejudiced by the widespread publicity which preceded the petitioner’s trial. One ingredient of this pretrial publicity was the telecast of the September hearings. Despite the confusion in the courtroom during those hearings, all that a potential juror could have possibly learned from watching them on television was that the petitioner’s case had been called for trial, and that motions had been made and acted upon for a continuance, and to exclude cameras and television. At those hearings, there was no discussion whatever of anything bearing on the petitioner’s guilt or innocence. This was conceded by the petitioner’s counsel at the trial. [ Footnote 5/8 ]
Because of our refusal to review the petitioner’s claim that pretrial publicity had a prejudicial effect upon the jurors in this case, and because, insofar as the September hearings were an element of that publicity, the claim is patently without merit, that issue is simply not here. Our decision in Rideau v. Louisiana, 373 U. S. 723 , therefore, has no bearing at all in this case. There, the record showed that the inhabitants of the small Louisiana parish where the trial was held had repeatedly been exposed to a television film showing
“Rideau, in jail, flanked by the sheriff and two state troopers, admitting in detail the commission of the robbery, kidnapping, and murder, in response to leading questions by the sheriff.”
373 U.S.
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at 373 U. S. 725 . We found that “[a]ny subsequent court proceedings in a community so pervasively exposed to such a spectacle could be but a hollow formality.” Id. at 373 U. S. 726 . See also Irvin v. Dowd, 366 U. S. 717 .
The Rideau case was no more than a contemporary application of enduring principles of procedural due process, principles reflected in such earlier cases as Moore v. Dempsey, 261 U. S. 86 ; Brown v. Mississippi, 297 U. S. 278 ; and Chambers v. Florida, 309 U. S. 227 , 309 U. S. 235 -241. “Under our Constitution’s guarantee of due process,” we said,
“a person accused of committing a crime is vouchsafed basic minimal rights. Among these are the right to counsel, the right to plead not guilty, and the right to be tried in a courtroom presided over by a judge.”
373 U.S. at 373 U. S. 726 -727. We had occasion to apply the same basic concepts of procedural due process earlier this Term in Turner v. Louisiana, 379 U. S. 466 .
“In the constitutional sense, trial by jury in a criminal case necessarily implies at the very least that the ‘evidence developed’ against a defendant shall come from the witness stand in a public courtroom where there is full judicial protection of the defendant’s right of confrontation, of cross-examination, and of counsel.”
379 U.S. at 379 U. S. 472 -473.
But we do not deal here with mob domination of a courtroom, with a kangaroo trial, with a prejudiced judge or a jury inflamed with bias. Under the limited grant of certiorari in this case, the sole question before us is an entirely different one. It concerns only the regulated presence of television and still photography at the trial itself, which began on October 22, 1962. Any discussion of pretrial events can do no more than obscure the important question which is actually before us.
III
It is obvious that the introduction of television and news cameras into a criminal trial invites many serious constitutional hazards. The very presence of photographers
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and television cameramen plying their trade in a courtroom might be so completely and thoroughly disruptive and distracting as to make a fair trial impossible . Thus, if the scene at the September hearing had been repeated in the courtroom during this jury trial, it is difficult to conceive how a fair trial in the constitutional sense could have been afforded the defendant. [ Footnote 5/9 ] And even if, as was true here, the television cameras are so controlled and concealed as to be hardly perceptible in the courtroom itself, there are risks of constitutional dimensions that lurk in the very process of televising court proceedings at all.
Some of those risks are catalogued in the amicus curiae brief filed in this case by the American Bar Association:
“[P]otential or actual jurors, in the absence of enforceable and effective safeguards, may arrive at certain misconceptions regarding the defendant and his trial by viewing televised pretrial hearings and motions from which the jury is ordinarily excluded. Evidence otherwise inadmissible may leave an indelible mark. . . . Once the trial begins, exposure to nightly rebroadcasts of selected portions of the day’s proceedings will be difficult to guard against, as jurors spend frequent evenings before the television set. The obvious impact of witnessing repeated trial episodes and hearing accompanying commentary, episodes admittedly chosen for their news value, and not for evidentiary purposes, can serve only to distort the jurors’ perspective. . . . Despite the court’s injunction not to discuss the case, it seems undeniable that jurors will be subject to the pressure of television-watching family, friends and, indeed, strangers. . . . It is not too much to imagine a juror being confronted with his wife’s television-oriented viewpoint. . . . Additionally, the jurors’ daily television appearances may make them recognizable celebrities, likely to be stopped by passing
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strangers, or perhaps harried by intruding telephone calls. . . .”
Constitutional problems of another kind might arise if a witness or juror were subjected to being televised over his objection.
The plain fact of the matter, however, is that none of these things happened or could have happened in this case. The jurors themselves were prevented from seeing any telecasts of the trial, and completely insulated from association with any members of the public who did see such telecasts. This case, therefore, does not remotely resemble Turner v. Louisiana, 379 U. S. 466 , where, during the trial, the jurors were subjected outside the courtroom to unmeasured and unmeasurable influences by key witnesses for the prosecution.
In the courtroom itself, there is nothing to show that the trial proceeded in any way other than it would have proceeded if cameras and television had not been present. In appearance, the courtroom was practically unaltered. There was no obtrusiveness and no distraction, no noise and no special lighting. There is no indication anywhere in the record of any disturbance whatever of the judicial proceedings. There is no claim that the conduct of the judge, or that any deed or word of counsel, or of any witness, or of any juror, was influenced in any way by the presence of photographers or by television.
Furthermore, from a reading of the record, it is crystal clear that this was not a trial where the judge was harassed or confused or lacking in command of the proceedings before the jury. Not once, after the first witness was called, was there any interruption at all of the trial proper to secure a ruling concerning the presence of cameramen in the courtroom. There was no occasion during the entire trial — until after the jury adjourned to reach its verdict — for any cautionary word to members of the press in the courtroom. The only time a motion was made, the jury was not in the courtroom. The trial itself was a
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most mundane affair, totally lacking in the lurid and completely emotionless. The evidence related solely to the circumstances in which various documents had been signed and negotiated. It was highly technical, if not downright dull. The petitioner called no witnesses, and counsel for petitioner made only a brief closing argument to the jury. There is nothing to indicate that the issues involved were of the kind where emotion could hold sway. The transcript of the trial belies any notion that frequent interruptions and inconsistent rulings communicated to the jury any sense that the judge was unable to concentrate on protecting the defendant and conducting the trial in a fair manner, in accordance with the State and Federal Constitutions.
IV
What ultimately emerges from this record, therefore, is one bald question — whether the Fourteenth Amendment of the United States Constitution prohibits all television cameras from a state courtroom whenever a criminal trial is in progress. In the light of this record and what we now know about the impact of television on a criminal trial, I can find no such prohibition in the Fourteenth Amendment or in any other provision of the Constitution. If what occurred did not deprive the petitioner of his constitutional right to a fair trial, then the fact that the public could view the proceeding on television has no constitutional significance. The Constitution does not make us arbiters of the image that a televised state criminal trial projects to the public.
While no First Amendment claim is made in this case, there are intimations in the opinions filed by my Brethren in the majority which strike me as disturbingly alien to the First and Fourteenth Amendments’ guarantees against federal or state interference with the free communication of information and ideas. The suggestion that there are limits upon the public’s right to know what goes on in
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the courts causes me deep concern. The idea of imposing upon any medium of communications the burden of justifying its presence is contrary to where I had always thought the presumption must lie in the area of First Amendment freedoms. See Speiser v. Randall, 357 U. S. 513 , 357 U. S. 525 . And the proposition that nonparticipants in a trial might get the “wrong impression” from unfettered reporting and commentary contains an invitation to censorship which I cannot accept. Where there is no disruption of the “essential requirement of the fair and orderly administration of justice,” “[f]reedom of discussion should be given the widest range.” Pennekamp v. Florida, 328 U. S. 331 , 328 U. S. 347 ; Bridges v. California, 314 U. S. 252 . Cf. Cox v. Louisiana, 379 U. S. 559 , 379 U. S. 563 .
I do not think that the Constitution denies to the State or to individual trial judges all discretion to conduct criminal trials with television cameras present, no matter how unobtrusive the cameras may be. I cannot say at this time that it is impossible to have a constitutional trial whenever any part of the proceedings is televised or recorded on television film. I cannot now hold that the Constitution absolutely bars television cameras from every criminal courtroom, even if they have no impact upon the jury, no effect upon any witness, and no influence upon the conduct of the judge.
For these reasons I would affirm the judgment.
[ Footnote 5/1 ]
Canons of Judicial Ethics. American Bar Association: Judicial Canon 35. Improper publicizing of Court proceedings.
“Proceedings in court should be conducted with fitting dignity and decorum. The taking of photographs in the courtroom, during sessions of the court or recesses between sessions, and the broadcasting or televising of court proceedings detract from the essential dignity of the proceedings, distract participants and witnesses in giving testimony, and create misconceptions with respect thereto in the mind of the public, and should not be permitted.”
“Provided that this restriction shall not apply to the broadcasting or televising, under the supervision of the court, of such portions of naturalization proceedings (other than the interrogation of applicants) as are designed and carried out exclusively as a ceremony for the purpose of publicly demonstrating in an impressive manner the essential dignity and the serious nature of naturalization.”
Canons of Judicial Ethics, Integrated State Bar of Texas: Judicial Canon 28. Improper Publicizing of Court Proceedings.
“Proceedings in court should be conducted with fitting dignity and decorum. The taking of photographs in the courtroom, during sessions of the court or recesses between sessions, and the broadcasting or televising of court proceedings unless properly supervised and controlled, may detract from the essential dignity of the proceedings, distract participants and witnesses in giving testimony, and create misconceptions with respect thereto in the mind of the public. The supervision and control of such trial coverage shall be left to the trial judge, who has the inherent power to exclude or control coverage in the proper case in the interest of justice.”
“In connection with the control of such coverage, the following declaration of principles is adopted:”
“(1) There should be no use of flashbulbs or other artificial lighting.”
“(2) No witness, over his expressed objection, should be photographed, his voice broadcast, or be televised.”
“(3) The representatives of news media must obtain permission of the trial judge to cover by photograph, broadcasting or televising, and shall comply with the rules prescribed by the judge for the exercise of the privilege.”
“(4) Any violation of the Court’s Rules shall be punished as a contempt.”
“(5) Where a judge has refused to allow coverage or has regulated it, any attempt, other than argument by representatives of the news media directly with the Court, to bring pressure of any kind on the judge pending final disposition of the cause in trial shall be punished as a contempt.”
[ Footnote 5/2 ]
A contemporary newspaper account described the scene as follows:
“A television motor van, big as an intercontinental bus, was parked outside the courthouse, and the second-floor courtroom was a forest of equipment. Two television cameras had been set up inside the bar, and four more marked cameras were aligned just outside the gates.”
“A microphone stuck its 12-inch snout inside the jury box, now occupied by an overflow of reporters from the press table, and three microphones confronted Judge Dunagan on his bench. [C]ables and wires snaked over the floor.”
The New York Times, September 25, 1962, p. 46, col. 4.
[ Footnote 5/3 ]
In ruling on the motion, the trial judge stated:
“In the past, it has been the policy of this Court to permit televising in the courtroom under the rules and supervision of the Court. Heretofore, I have not encountered any difficulty with it. I was unable to observe any detraction from the witnesses or the attorneys in those cases. We have watched television, of course, grow up from its infancy and now into its maturity, and it is a news media. So I really do not see any justified reason why it should not be permitted to take its proper seat in the family circle. However, it will be under the strict supervision of the Court. I know there has been pro and con about televising in the courtroom. I have heard some say that it makes a circus out of the Court. I had the privilege yesterday morning of sitting in my home and viewing a sermon by the First Baptist Church over in Dallas, and certainly it wasn’t any circus in that church; and I feel that if it is a proper instrument in the house of the Lord, it is not out of place in the courtroom, if properly supervised.”
“Now, television is going to be televising whatever the scene is here. If you want to watch a ball game and that is what they televise, you are going to see a ball game. If you want to see a preacher and hear a sermon, you tune in on that, and that is what you are going to get. If the Court permits a circus in this courtroom, it will be televised, that is true, but they will not be creating a circus.”
“Now, the most important point is whether or not it would interfere with a fair and impartial trial of this Defendant. That is the most important point, and that is the purpose, or will be the primary purpose of the Court, to insure that he gets that fair trial.”
“There is not anything the Court can do about the interest in this case, but I can control your activities and your conduct here; and I can assure you now that this Court is not going to be turned into a circus — with TV or without it. Whatever action is necessary for the Court to take to insure that, the Court will take it.”
“ * * * *”
“There has been one consideration that the Court has given, and it is that this is a small courtroom, and there will be hundreds of people trying to get into this courtroom to witness this trial. I believe we would have less confusion if they would stay at home and stay out of the courtroom and look in on the trial. With all of those people trying to crowd in and push into this courtroom, that is another consideration I have given to it.”
[ Footnote 5/4 ]
“In my statement of September 24, 1962, admitting television and other cameras in the courtroom during the trial of Billie Sol Estes, I said cameras would be allowed under the control and direction of the Court so long as they did not violate the legal rights of the Defendant or the State of Texas.”
“In line with my statement of September 24, 1962, I am at this time informing both television and radio that live broadcasting or telecasting by either news media cannot and will not be permitted during the interrogation of jurors in testing their qualifications, or of the testimony given by the witnesses, as to do so would be in violation of Art. 644 of the Code of Criminal Procedure of Texas, which provides as follows:”
” At the request of either party, the witnesses on both sides may be sworn and placed in the custody of an officer and removed out of the courtroom to some place where they can not hear the testimony as delivered by any other witness in the case. This is termed placing witnesses under rule.”
“. . . [E]ach television network and the local television station will be allowed one film camera without sound in the courtroom, and the film will be made available to other television stations on a pool basis. Marshall Pengra, manager of Television Station KLTV, Tyler, will be in charge of the independent pool, and independent stations may contact him. The same will be true of cameras for the press, which will be limited to the local press, Associated Press, and United Press.”
“I am making this statement at this time in order that the two news media affected may have sufficient notice before the case is called on October 22nd.”
“The rules I have set forth above concerning the use of cameras are subject to change if I find that they are too restrictive or not workable, for any reason.”
[ Footnote 5/5 ]
There were nine witnesses for the prosecution, and no witnesses for the defense.
[ Footnote 5/6 ]
Arts. 668, 745 and 725, Tex.Code Crim.Proc.
[ Footnote 5/7 ]
Petition for Writ of Certiorari, Question 3, p. 3.
[ Footnote 5/8 ]
“A. (Mr. Hume Cofer, counsel for petitioner). . . . The publicity that was given this trial on the last occasion and the number of cameras here, I think was sufficient to spread the news of this case throughout the county, to every available juror; and it is my opinion that, on that occasion, there were so many cameras and so much paraphernalia here that it gave an opportunity for every prospective juror in Smith County to know about this case.”
“Q. Not about the facts of the case?”
“A. No, sir; not about the facts, nor any of the evidence.”
[ Footnote 5/9 ]
See <l=|381 u.s.=”” 532fn5=”” 2|=””>note 2.</l=|381>
MR. JUSTICE WHITE, with whom MR. JUSTICE BRENNAN joins, dissenting.
I agree with MR. JUSTICE STEWART that a finding of constitutional prejudice on this record entails erecting a flat ban on the use of cameras in the courtroom, and believe that it is premature to promulgate such a broad constitutional principle at the present time. This is the first case in this Court dealing with the subject of television
Home Page 381 U. S. 616
coverage of criminal trials; our cases dealing with analogous subjects are not really controlling, cf. Rideau v. Louisiana, 373 U. S. 723 , and there is, on the whole, a very limited amount of experience in this country with television coverage of trials. In my view, the currently available materials assessing the effect of cameras in the courtroom are too sparse and fragmentary to constitute the basis for a constitutional judgment permanently barring any and all forms of television coverage. As was said in another context, “we know too little of the actual impact . . . to reach a conclusion on the bare bones of the . . . evidence before us.” White Motor Co. v. United States, 372 U. S. 253 , 372 U. S. 261 . It may well be, however, that, as further experience and informed judgment do become available, the use of cameras in the courtroom, as in this trial, will prove to pose such a serious hazard to a defendant’s rights that a violation of the Fourteenth Amendment will be found without a showing on the record of specific demonstrable prejudice to the defendant. Compare Wolf v. Colorado, 338 U. S. 25 , with Mapp v. Ohio, 367 U. S. 643 ; Betts v. Brady, 316 U. S. 455 , with Gideon v. Wainwright, 372 U. S. 335 ; Stein v. New York, 346 U. S. 156 , with Jackson v. Denno, 378 U. S. 368 , 378 U. S. 389 -390.
The opinion of the Court in effect precludes further opportunity for intelligent assessment of the probable hazards imposed by the use of cameras at criminal trials. Serious threats to constitutional rights in some instances justify a prophylactic rule dispensing with the necessity of showing specific prejudice in a particular case. Rideau v. Louisiana, 373 U. S. 723 , 373 U. S. 727 ; Jackson v. Denno, 378 U. S. 368 , 378 U. S. 389 . But these are instances in which there has been ample experience on which to base an informed judgment. Here, although our experience is inadequate and our judgment correspondingly infirm, the Court discourages further meaningful study of the use of television at criminal trials. Accordingly, I dissent.
Home Page 381 U. S. 617
MR. JUSTICE BRENNAN.
I write merely to emphasize that only four of the five Justices voting to reverse rest on the proposition that televised criminal trials are constitutionally infirm whatever the circumstances. Although the opinion announced by my Brother CLARK purports to be an “opinion of the Court,” my Brother HARLAN subscribes to a significantly less sweeping proposition. He states:
“The Estes trial was a heavily publicized and highly sensational affair. I therefore put aside all other types of cases. . . . The resolution of those further questions should await an appropriate case; the Court should proceed only step by step in this unplowed field. The opinion of the Court necessarily goes no farther, for only the four members of the majority who unreservedly join the Court’s opinion would resolve those questions now. ”
Ante, pp. 381 U. S. 590 -591. (Emphasis supplied.)
Thus, today’s decision is not a blanket constitutional prohibition against the televising of state criminal trials.
While I join the dissents of my Brothers STEWART and WHITE, I do so on the understanding that their use of the expressions “the Court’s opinion” or “the opinion of the Court” refers only to those views of our four Brethren which my Brother HARLAN explicitly states he shares.
Contributors and Attributions
- Authored by : US Government. Located at : https://supreme.justia.com/cases/federal/us/381/532/case.html . License : Public Domain: No Known Copyright


7.3D: Vitamin B₅ (Pantothenic acid)
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Pantothenic acid, also called vitamin B 5 , is a water-soluble vitamin. Pantothenic acid is an essential nutrient. Animals require pantothenic acid to synthesize coenzyme-A (CoA), as well as to synthesize and metabolize proteins, carbohydrates, and fats. Pantothenic acid is the amide between pantoic acid and β-alanine. Its name derives from the Greek pantothen , meaning "from everywhere", and small quantities of pantothenic acid are found in nearly every food, with high amounts in fortified whole-grain cereals, egg yolks, liver and dried mushrooms. It is commonly found as its alcohol analog, the provitamin panthenol (pantothenol), and as calcium pantothenate.
Skeletal formula of (R)-pantothenic acid
Dietary Sources
Content of pantothenic acid varies among manufactured and natural foods, especially fortified ready-to-eat cereals, infant formulas, energy bars and dried foods. Major food sources of pantothenic acid are dried mushrooms, liver, dried egg yolks and sunflower seeds. Whole grains are another good source of the vitamin, but milling removes much of the pantothenic acid, as it is found in the outer layers of whole grains. In animal feeds, the most important sources are alfalfa, cereal, fish meal, peanut meal, molasses, mushrooms, rice, wheat bran, and yeasts.
Dietary Reference Intake
The Food and Nutrition Board of the U.S. Institute of Medicine updated Estimated Average Requirements (EARs) and Recommended Dietary Allowances (RDAs) for B vitamins in 1998. At that time there was not sufficient information to establish EARs and RDAs for pantothenic acid. In instances such as this, the Board sets Adequate Intakes (AIs), with the understanding that at some later date, AIs will be replaced by more exact information. As for safety, the FNB sets Tolerable Upper Intake Levels (known as ULs) for vitamins and minerals when evidence is sufficient. In the case of pantothenic acid there is no UL, as there is insufficient human data to identify adverse effects from high doses. The European Food Safety Authority reviewed the same safety question and also reached the conclusion that there was not sufficient evidence to set a UL for pantothenic acid. Collectively the EARs, RDAs and ULs are referred to as Dietary Reference Intakes.
For U.S. food and dietary supplement labeling purposes the amount in a serving is expressed as a percent of Daily Value (%DV). For pantothenic acid labeling purposes 100% of the Daily Value was 10 mg, but as of May 2016 it has been revised to 5 mg. Food and supplement companies have until July 2018 to comply with the change.
| Age group | Age | Adequate intake |
|---|---|---|
| Infants | 0–6 months | 1.7 mg |
| Infants | 7–12 months | 1.8 mg |
| Children | 1–3 years | 2 mg |
| Children | 4–8 years | 3 mg |
| Children | 9–13 years | 4 mg |
| Adult men and women | 14+ years | 5 mg |
| Pregnant women | (vs. 5) | 6 mg |
| Breastfeeding women | (vs. 5) | 7 mg |
Toxicity of pantothenic acid is unlikely. In fact, no Tolerable Upper Level Intake (UL) has been established for the vitamin. Large doses of the vitamin, when ingested, have no reported side effects and massive doses (e.g., 10 g/day) may only yield mild intestinal distress, and diarrhea at worst. It has been suggested, however, that high doses of pantothenic acid might worsen panic attacks in those with panic disorder by prolonging the duration until adrenal exhaustion. Pantothenic acid, at a human equivalent dose within the range of common supplementation, was shown to induce adrenal hyper-responsiveness to stress stimulation. There are also no adverse reactions known following parenteral (injected) or topical (skin) applications of the vitamin.
Absorption
When found in foods, most pantothenic acid is in the form of CoA or acyl carrier protein (ACP). For the intestinal cells to absorb this vitamin, it must be converted into free pantothenic acid. Within the lumen of the intestine, CoA and ACP are hydrolyzed into 4'-phosphopantetheine. The 4'-phosphopantetheine is then dephosphorylated into pantetheine. Pantetheinase, an intestinal enzyme, then hydrolyzes pantetheine into free pantothenic acid. Free pantothenic acid is absorbed into intestinal cells via a saturable, sodium-dependent active transport system. At high levels of intake, when this mechanism is saturated, some pantothenic acid may also be absorbed via passive diffusion. As intake increases 10-fold, however, absorption rate decreases to 10%.
Deficiency
Pantothenic acid deficiency is exceptionally rare and has not been thoroughly studied. In the few cases where deficiency has been seen (victims of starvation and limited volunteer trials), nearly all symptoms can be reversed with the return of pantothenic acid. Symptoms of deficiency are similar to other vitamin B deficiencies. There is impaired energy production, due to low CoA levels, which could cause symptoms of irritability, fatigue, and apathy.Acetylcholine synthesis is also impaired; therefore, neurological symptoms can also appear in deficiency; they include numbness, paresthesia, and muscle cramps. Deficiency in pantothenic acid can also cause hypoglycemia, or an increased sensitivity to insulin. Insulin receptors are acylated with palmitic acid when they do not want to bind with insulin. Therefore, more insulin will bind to receptors when acylation decreases, causing hypoglycemia. Additional symptoms could include restlessness, malaise, sleep disturbances, nausea, vomiting, and abdominal cramps. In a few rare circumstances, more serious (but reversible) conditions have been seen, such as adrenal insufficiency and hepatic encephalopathy.
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- Wikipedia. Content is copyrighted under a CC-BY-SA 4.0 license.


2.12: Introduction to Categorical vs. Quantitative Data
What you’ll learn to do: Distinguish between quantitative and categorical variables in context.
In studying real world phenomena, we encounter many different types of data. Some data is a measurement: such as temperature, height, or volume. Other data may be a label: such as male or female, country name, or patient ID number. How we statistically analyze the data depends on the type of data we are collecting. Since quantitative data is numerical, there are clear numerical ways compute “averages”, “spread”, and shape of data when graphed. For qualitative data, we will look at counts and proportions to give a numerical way to measure these qualitative data which do not have a numeric meaning.
Contributors and Attributions
CC licensed content, Shared previously
- Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution


2.5: Make commitments that support teamwork
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In this module, you will review some key concepts about becoming an effective team, presented within the infographic below. If you prefer a more traditional reading experience, scroll below the interactive graphic for the full text. You can also download a copy of this infographic for your reference.
Image Credit: Rawia Inaim
A Team is two or more people; working together; on a Common Goal (or goals). Groups become Teams if the common goals are clear and attention is paid to both interpersonal and task functions.
Each Team must set up their own guidelines for good communication and a Team Charter. Through discussion and negotiation the members choose the items that are most important for their clear communication as a Team. These often include commitment to:
Early in the formation of the group, the members must decide what will be measured in the process. These items are generally critical to success and for the group to become an Effective Team. A team that has succeeded shares the following characteristics. Its members:
What have we done (individually and collectively) to meet our goals and keep the Team Charter?
How can we do better for next time? (Next steps)
Celebrate what you have accomplished and then refocus your efforts for greater success!
Your personal beliefs are the core values that affect and drive how you look at the world, your behaviour in the world and your interaction with others. They are how you do “business” with the rest of the world. In other words, they are the basis for everything that you are and do. These beliefs about appropriate behaviours, attitudes and strategies also guide every working group and need to be explicit and understood.
It is useful to know what you are expected to do in a group situation. This is often delivered or requested from an administrative or political level and appears in the form of a “job description”. The group which is mandated may not be able to effect the general outline of the mandate. The context in which the group operates has critical effects on what can be done.
A mission statement embodies the group’s current purpose and intent and answers (within the mandate of the group) questions such as: What are we about? Why are we working together? What do we want to achieve? It describes the business that you are in. This may be a statement developed by the whole organization or it may be more localized in a department, program, class, work group or individually. It gives direction to actions. Without knowing your mission, you may not be able to get started.
Vision is a future oriented statement of a group’s purpose in a task, project or work team. Having the members shared a vision that aligns with their personal values and aspirations is a solid basis for production. Time spent at the beginning in dreaming and discussing what the final result will be is time well spent. If it is not possible to have a shared vision of the end product and the goals and milestones that must be reached then the team may also have difficulty identifying whether they have accomplished their purpose.
Sometimes, when the project is open ended or ongoing, the final product cannot be totally “visioned” at the beginning. A shared vision will then be one that all of the team members agree are the elements of where they want to get at this time and the direction that they will start moving towards to achieve these elements.
Visions should be revisited and refined over time. If the team is not heading in the same direction, then it may not get anywhere.
What are the individual tasks and goals that will build to making your vision manifest? Goals lead towards the realization of the vision. It is important to develop appropriate goals, make them explicit and share an understanding of each one.
Goals have:
Like our vision statement, goals need to be realigned with reality on a regular basis. Evaluation and adjustment drive this process.
Knowing where you are going and how you intend to get there is a good start. The final step is continuous improvement. Planning, implementation, and verification are tools for analysis and change as the process unfolds. Improvement is continual but the steps are small. Pick changes that can be made now that will have a positive effect – 1% is enough each time.


 This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs.
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- 2.1: Prelude to Descriptive Statistics
- In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs, as well as frequency polygons, and time series graphs. Our emphasis will be on histograms and box plots.
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- 2.2: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
- A stem-and-leaf plot is a way to plot data and look at the distribution, where all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends. A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories.
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- 2.3: Histograms, Frequency Polygons, and Time Series Graphs
- A histogram is a graphic version of a frequency distribution. The graph consists of bars of equal width drawn adjacent to each other. The horizontal scale represents classes of quantitative data values and the vertical scale represents frequencies. The heights of the bars correspond to frequency values. Histograms are typically used for large, continuous, quantitative data sets. A frequency polygon can also be used when graphing large data sets with data points that repeat.
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- 2.4: Measures of the Location of the Data
- The values that divide a rank-ordered set of data into 100 equal parts are called percentiles and are used to compare and interpret data. For example, an observation at the 50th percentile would be greater than 50 % of the other obeservations in the set. Quartiles divide data into quarters. The first quartile is the 25th percentile, the second quartile is 50th percentile, and the third quartile is the the 75th percentile. The interquartile range is the range of the middle 50 % of the data values
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- 2.5: Box Plots
- Box plots are a type of graph that can help visually organize data. To graph a box plot the following data points must be calculated: the minimum value, the first quartile, the median, the third quartile, and the maximum value. Once the box plot is graphed, you can display and compare distributions of data.
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- 2.6: Measures of the Center of the Data
- The mean and the median can be calculated to help you find the "center" of a data set. The mean is the best estimate for the actual data set, but the median is the best measurement when a data set contains several outliers or extreme values. The mode will tell you the most frequently occurring datum (or data) in your data set. The mean, median, and mode are extremely helpful when you need to analyze your data.
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- 2.7: Skewness and the Mean, Median, and Mode
- Looking at the distribution of data can reveal a lot about the relationship between the mean, the median, and the mode. There are three types of distributions. A right (or positive) skewed distribution, a left (or negative) skewed distribution and a symmetrical distribution.
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- 2.8: Measures of the Spread of the Data
- An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation. The standard deviation is a number that measures how far data values are from their mean.
Contributors and Attributions
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Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


6.1: Basic Facts about Eigenvalue Problems
Even if a matrix \(\mathbf{A}\) is real, its eigenvectors and eigenvalues can be complex. For example,
\[\begin{bmatrix}1&1\\-1&1\end{bmatrix} \begin{bmatrix}1\\i\end{bmatrix} = (1+i) \begin{bmatrix}1\\i\end{bmatrix}.\]
Eigenvectors are not uniquely defined. Given an eigenvector \(\vec{x}\), any nonzero complex multiple of that vector is also an eigenvector of the same matrix, with the same eigenvalue. We can reduce this ambiguity by normalizing eigenvectors to a fixed unit length:
\[\sum_{n=0}^{N-1} |x_n|^2 = 1.\]
Note, however, that even after normalization, there is still an inherent ambiguity in the overall complex phase. Multiplying a normalized eigenvector by any phase factor \(e^{i\phi}\) gives another normalized eigenvector with the same eigenvalue.
6.1.1 Matrix Diagonalization
Most matrices are diagonalizable , meaning that their eigenvectors span the \(N\)-dimensional complex space (where \(N\) is the matrix size). Matrices which are not diagonalizable are called defective . Many classes of matrices that are relevant to physics (such as Hermitian matrices) are always diagonalizable; i.e., never defective.
The reason for the term "diagonalizable" is as follows. A diagonalizable \(N\times N\) matrix \(\mathbf{A}\) has eigenvectors that span the \(N\)-dimensional space, meaning that we can choose \(N\) linearly independent eigenvectors, \(\{\vec{x}_0, \vec{x}_1, \cdots \vec{x}_{N-1}\}\), with eigenvalues \(\{\lambda_0, \lambda_1, \cdots \lambda_{N-1}\}\). We refer to such a set of \(N\) eigenvalues as the "eigenvalues of \(\mathbf{A}\)". If we group the eigenvectors into an \(N\times N\) matrix
\[\mathbf{Q} = [\vec{x}_0, \vec{x}_1, \cdots \vec{x}_{N-1}],\]
then, since the eigenvectors are linearly independent, \(\mathbf{Q}\) is guaranteed to be invertible. Using the eigenvalue equation, we can then show that
\[\mathbf{Q}^{-1} \,\mathbf{A} \, \mathbf{Q} = \begin{bmatrix}\lambda_0 & 0& \cdots & 0 \\ 0 & \lambda_1 & \cdots & 0 \\ \vdots& \vdots & \ddots & \vdots \\ 0&0&\cdots&\lambda_{N-1}\end{bmatrix}.\]
In other words, there exists a similarity transformation which converts \(\mathbf{A}\) into a diagonal matrix. The \(N\) numbers along the diagonal are precisely the eigenvalues of \(\mathbf{A}\).
6.1.2 The Characteristic Polynomial
One of the most important consequences of diagonalizability is that the determinant of a diagonalizable matrix \(\mathbf{A}\) is the product of its eigenvalues:
\[\det(\mathrm{A}) = \prod_{n=0}^{N-1} \lambda_n\]
This can be proven by taking the determinant of the similarity transformation equation, and using (i) the property of the determinant that \(\det(\mathbf{U}\mathbf{V}) = \det(\mathbf{U})\det(\mathbf{V})\), and (ii) the fact that the determinant of a diagonal matrix is the product of the elements along the diagonal.
In particular, the determinant of \(\mathbf{A}\) is zero if one of its eigenvalues is zero. This fact can be further applied to the following re-arrangement of the eigenvalue equation:
\[\Big(\mathbf{A} - \lambda\mathbf{I}\Big) \, \vec{x} = 0,\]
where \(\mathbf{I}\) is the \(N\times N\) identity matrix. This says that the matrix \(\mathbf{A}-\lambda\mathbf{I}\) has an eigenvalue of zero, meaning that for any eigenvalue \(\lambda\),
\[\det\left(\mathbf{A} - \lambda\mathbf{I}\right) = 0.\]
The left-hand side of the above equation is a polynomial in the variable \(\lambda\), of degree \(N\). This is called the characteristic polynomial of the matrix \(\mathbf{A}\). Its roots are eigenvalues of \(\mathbf{A}\), and vice versa.
For \(2\times 2\) matrices, the standard way of calculating the eigenvalues is to find the roots of the characteristic polynomial. However, this is not a reliable method for finding the eigenvalues of larger matrices. There is a well-known and important result in mathematics, known as Abel's impossibility theorem , which states that polynomials of degree \(5\) and higher have no general algebraic solution. (By comparison, degree-2 polynomials have a general algebraic solution, which is the familiar quadratic formula, and similar formulas exist for degree-3 and degree-4 polynomials.) A matrix of size \(N \ge 5\) has a characteristic polynomial of degree \(N \ge 5\), and Abel's impossibility theorem tells us that we can't calculate the roots of that characteristic polynomial by ordinary arithmetic.
In fact, Abel's impossibility theorem leads to an even stronger conclusion: there is no general algebraic method for finding the eigenvalues of a matrix of size \(N \ge 5\), whether using the characteristic polynomial or any other method . For suppose we had such a method for finding the eigenvalues of a matrix. Then, for any polynomial equation of degree \(N \ge 5\), of the form
\[a_0 + a_1 \lambda + \cdots + a_{N-1} \lambda^{N-1} + \lambda^N = 0,\]
we can construct an \(N\times N\) "companion matrix" of the form
\[\mathbf{A} = \begin{bmatrix}0 & 1 & 0 & \cdots & 0 \\ 0 & 0 & 1& \cdots & 0 \\ \vdots&\vdots&\ddots&\ddots& \vdots \\ 0&0&0&\ddots&1\\-a_0& -a_1& -a_2 & \cdots & -a_{N-1} \end{bmatrix}.\]
As you can check for yourself, each root \(\lambda\) of the polynomial is also an eigenvalue of the companion matrix, with corresponding eigenvector
\[\vec{x} = \begin{bmatrix}1\\\lambda\\ \vdots \\ \lambda^{N-1}\end{bmatrix}.\]
Hence, if there exists a general algebraic method for finding the eigenvalues of a large matrix, that would allow us to find solve polynomial equations of high degree. Abel's impossibility theorem tells us that no such solution method can exist.
This might seem like a terrible problem, but in fact there's a way around it, as we'll shortly see.
6.1.3 Hermitian Matrices
A Hermitian matrix \(\mathbf{H}\) is a matrix which has the property
\[\mathbf{H}^\dagger = \mathbf{H},\]
where \(\mathbf{H}^\dagger\) denotes the "Hermitian conjugate", which is matrix transposition accompanied by complex conjugation:
\[\mathbf{H}^\dagger \equiv \left(\mathbf{H}^T\right)^*, \quad \mathrm{i.e.}\;\;\left(H^\dagger\right)_{ij} = H_{ji}^*.\]
Hermitian matrices have the nice property that all their eigenvalues are real. This can be easily proven using index notation:
\[\begin{align}\sum_j H_{ij} x_j = \lambda x_i \;\;&\Rightarrow\;\; \sum_j x_j^* H_{ji} = \lambda^* x_i^*\\ &\Rightarrow \sum_{ij} x^*_i H_{ij} x_j = \lambda \sum_i |x_i|^2 = \lambda^* \sum_j |x_j|^2 \\ &\Rightarrow \lambda = \lambda^*.\end{align}\]
In quantum mechanics, Hermitian matrices play a special role: they represent measurement operators, and their eigenvalues (which are restricted to the real numbers) are the set of possible measurement outcomes.